On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions

Igor Bock; Ivan Hlaváček; Ján Lovíšek

Aplikace matematiky (1984)

  • Volume: 29, Issue: 4, page 303-314
  • ISSN: 0862-7940

Abstract

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A control of the system of nonlinear Kármán's equations for a thin elastic plate with clamped edge is considered. The transversal loading plays the role of the control variable. The set of admissible controls is chosen in a way guaranteeing the unique solvability of the state function with respect to the control variable is proved. A disscussion of uniqueness of the optimal control and some necessary conditions of optimality are presented.

How to cite

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Bock, Igor, Hlaváček, Ivan, and Lovíšek, Ján. "On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions." Aplikace matematiky 29.4 (1984): 303-314. <http://eudml.org/doc/15360>.

@article{Bock1984,
abstract = {A control of the system of nonlinear Kármán's equations for a thin elastic plate with clamped edge is considered. The transversal loading plays the role of the control variable. The set of admissible controls is chosen in a way guaranteeing the unique solvability of the state function with respect to the control variable is proved. A disscussion of uniqueness of the optimal control and some necessary conditions of optimality are presented.},
author = {Bock, Igor, Hlaváček, Ivan, Lovíšek, Ján},
journal = {Aplikace matematiky},
keywords = {nonlinear Kármán equations; transversal loading; Dirichlet boundary conditions; Existence of optimal control; differentiability; state function; nonlinear Kármán equations; transversal loading; Dirichlet boundary conditions; Existence of optimal control; differentiability; state function},
language = {eng},
number = {4},
pages = {303-314},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions},
url = {http://eudml.org/doc/15360},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Bock, Igor
AU - Hlaváček, Ivan
AU - Lovíšek, Ján
TI - On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 4
SP - 303
EP - 314
AB - A control of the system of nonlinear Kármán's equations for a thin elastic plate with clamped edge is considered. The transversal loading plays the role of the control variable. The set of admissible controls is chosen in a way guaranteeing the unique solvability of the state function with respect to the control variable is proved. A disscussion of uniqueness of the optimal control and some necessary conditions of optimality are presented.
LA - eng
KW - nonlinear Kármán equations; transversal loading; Dirichlet boundary conditions; Existence of optimal control; differentiability; state function; nonlinear Kármán equations; transversal loading; Dirichlet boundary conditions; Existence of optimal control; differentiability; state function
UR - http://eudml.org/doc/15360
ER -

References

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  1. P. G. Ciarlet P. Rabier, Les équations de von Kármán, Springer Verlag, Berlin 1980. (1980) Zbl0433.73019MR0595326
  2. J. L. Lions, Sur le contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles, Dunod, Gauthier-Villars 1968. (1968) Zbl0179.41801MR0244606
  3. L. A. Ljusternik V. I. Sobolev, The elements of functional analysis, (in Russian). Moskva, Nauka 1965. (1965) MR0209802
  4. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Praha 1967. (1967) MR0227584

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